Rackwitz-Fiessler method and Nataf-Pearson method are two most widely used random space transformation methods. However, unlike Nataf-Pearson method, Rackwtitz-Fissler method is always used when random variables are independent due to its difficulties of accounting for dependency variation. So in present article, we discussed the transformation ways and linear correlation variations of these two methods. And found that the same isoprobabilitic transformation principle was followed by the forward transformation of Rackwitz-Fiessler method like that of the Nataf-Pearson method, so the same Pearson linear correlation matrix should also be possessed by the transformed random vector after the Rackwitz-Fiessler method. In addition, the backward transformations, algorithm realizations, computation cost and efficiency were also discussed between these two methods. Finally, combined with standard Hasofer-Lind FORM method, we presented two numerical examples to illustrate the actual differences and similarities of these two transformation methods in their reliability applications.

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